CN104202143A - Four-dimensional balance point-free hyperchaotic system based on five-simplest chaotic system, and analogue circuit - Google Patents

Four-dimensional balance point-free hyperchaotic system based on five-simplest chaotic system, and analogue circuit Download PDF

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CN104202143A
CN104202143A CN201410438026.4A CN201410438026A CN104202143A CN 104202143 A CN104202143 A CN 104202143A CN 201410438026 A CN201410438026 A CN 201410438026A CN 104202143 A CN104202143 A CN 104202143A
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CN104202143B (en
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王春梅
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STATE GRID ZHEJIANG YUEQING POWER SUPPLY Co Ltd
Yueqing Power Repair Manufacture Factory
State Grid Corp of China SGCC
State Grid Zhejiang Electric Power Co Ltd
Wenzhou Power Supply Co of State Grid Zhejiang Electric Power Co Ltd
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    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/001—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols using chaotic signals
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols

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Abstract

The invention provides a four-dimensional balance point-free hyperchaotic system based on a five-simplest three-dimensional chaotic system, and an analogue circuit. An operational amplifier U1, an operational amplifier U2, a resistor and a capacitor are adopted to form an inverse adder and an inverse integrator; multipliers U3 and U4 are adopted to realize multiplication; an 8V DC power source is used for realizing constant inputting; the model number of the operational amplifier U1 and the operational amplifier U2 is LF347N, while the model number of the multipliers U3 and U4 is AD633JN; the operational amplifier U1 is connected with the operational amplifier U2 and the multiplier U3; the operational amplifier U2 is connected with the multiplier U4, the DC power source and the operational amplifier U1; the multiplier U3 is connected with the operational amplifier U1, while the multiplier U4 is connected with the operational amplifier U2; the 8V DC power source is connected with the operational amplifier U2. The balance point-free four-dimensional hyperchaotic system is provided on the basis of the five-simplest three-dimensional chaotic system and realized by use of the analogue circuit; as a result, a new method and a new idea are provided for the application of the chaotic system in the engineering fields such as communication.

Description

Based on five the four-dimension of simple chaos system without balance point hyperchaotic system and analog circuit
Technical field
The present invention relates to a chaos system and analog circuit, particularly one based on five the four-dimension of simple chaos system without balance point hyperchaotic system and analog circuit.
Background technology
At present, the hyperchaotic system that oneself has is generally on the basis of three-dimensional chaotic system with three balance points, increase one dimension, formation has the four-dimensional hyperchaotic system that has a balance point at least, four-dimensional hyperchaotic system without balance point is not also suggested, the present invention is at five on the basis of simple three-dimensional chaotic system, a four-dimensional hyperchaotic system without balance point has been proposed, and realize with analog circuit, be applied to the engineering fields such as communication for chaos system a kind of new method and thinking are provided.
Summary of the invention
The technical problem to be solved in the present invention be to provide a kind of based on five the simplest chaos system without balance point hyperchaotic system and analog circuit, the present invention adopts following technological means to realize goal of the invention:
1, based on five the four-dimension of simple system without balance point hyperchaotic system, it is characterized in that being, comprise the following steps:
(1) five three-dimensional chaos chaos system i the simplest is:
dx / dt = a ( y - x ) dy / dt = - xz dz / dt = - b + xy i a = 5 , b = 90
(2) on the basis of three-dimensional chaotic system i, increase a differential equation dw/dt=-ky, and w is fed back on second equation of system i, obtain chaos system ii
dz / dt = a ( y - x ) dy / dt = w - xz dz / dt = - b + xy dw / dt = - xy ii a = 10 , b = 80 , k = 10
(3) according to without balance point hyperchaotic system ii constructing analog Circuits System, utilize operational amplifier U1, operational amplifier U2 and resistance and electric capacity to form anti-phase adder and inverting integrator, utilize multiplier U3 and U4 to realize multiplying, utilize 8V DC power supply to realize constant input, described operational amplifier U1 and operational amplifier U2 adopt LF347N, and described multiplier U3 and U4 adopt AD633JN;
Described operational amplifier U1 concatenation operation amplifier U2, multiplier U3, described operational amplifier U2 connects multiplier U4, DC power supply and operational amplifier U1, described multiplier U3 concatenation operation amplifier U1, described multiplier U4 concatenation operation amplifier U2, described 8V DC power supply concatenation operation amplifier U2;
The 1st pin of described operational amplifier U1 joins by resistance R 6 and the 2nd pin, join by resistance R 7 and the 6th pin, the 3rd, 5, 10, 12 pin ground connection, the 4th pin meets VCC, the 11st pin meets VEE, the 6th pin joins by capacitor C 2 and the 7th pin, the 7th pin meets output y, join by resistance R 1 and the 13rd pin, join by resistance R 13 and the 6th pin of U2, connect the 3rd pin of multiplier U4, the 8th pin output x, join by capacitor C 1 and the 9th pin, connect the 1st pin of multiplier U3, connect the 1st pin of multiplier U4, join by resistance R 4 and the 9th pin, the 13rd pin joins by resistance R 2 and the 14th pin, the 14th pin joins by resistance R 3 and the 9th pin,
The 1st, 2 pins of described operational amplifier U2 are unsettled, 3rd, 5,10,12 pin ground connection, the 4th pin meets VCC, the 11st pin meets VEE, the 6th pin joins by capacitor C 4 and the 7th pin, the 7th pin output w, join by resistance R 5 and the 2nd pin of U1, the 8th pin meets output z, connect the 3rd pin of multiplier U3, the 9th pin joins by capacitor C 3 and the 8th pin, connects ground connection after 8V DC power supply by resistance R 12, the 13rd pin joins by resistance R 10 and the 14th pin, and the 14th pin joins by resistance R 11 and the 9th pin;
The 1st pin of described multiplier U3 connects the 8th pin of U1, and the 3rd pin connects the 8th pin of U2, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, and the 7th pin connects U1 the 6th pin by resistance R 8, and the 8th pin meets VCC;
The 1st pin of described multiplier U4 connects the 8th pin of U1, and the 3rd pin connects the 7th pin of U1, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, and the 7th pin connects U2 the 13rd pin by resistance R 9, and the 8th pin meets VCC.
2, based on five the four-dimension of simple system without the analog circuit of balance point hyperchaotic system, it is characterized in that being, formed by operational amplifier U1, operational amplifier U2 and multiplier U3, multiplier U4 and 8V DC power supply;
Described operational amplifier U1 concatenation operation amplifier U2, multiplier U3, described operational amplifier U2 connects multiplier U4, DC power supply and operational amplifier U1, described multiplier U3 concatenation operation amplifier U1, described multiplier U4 concatenation operation amplifier U2, described 8V DC power supply concatenation operation amplifier U2, described operational amplifier U1 and operational amplifier U2 adopt LF347N, and described multiplier U3 and U4 adopt AD633JN;
The 1st pin of described operational amplifier U1 joins by resistance R 6 and the 2nd pin, join by resistance R 7 and the 6th pin, the 3rd, 5, 10, 12 pin ground connection, the 4th pin meets VCC, the 11st pin meets VEE, the 6th pin joins by capacitor C 2 and the 7th pin, the 7th pin meets output y, join by resistance R 1 and the 13rd pin, join by resistance R 13 and the 6th pin of U2, connect the 3rd pin of multiplier U4, the 8th pin output x, join by capacitor C 1 and the 9th pin, connect the 1st pin of multiplier U3, connect the 1st pin of multiplier U4, join by resistance R 4 and the 9th pin, the 13rd pin joins by resistance R 2 and the 14th pin, the 14th pin joins by resistance R 3 and the 9th pin,
The 1st, 2 pins of described operational amplifier U2 are unsettled, 3rd, 5,10,12 pin ground connection, the 4th pin meets VCC, the 11st pin meets VEE, the 6th pin joins by capacitor C 4 and the 7th pin, the 7th pin output w, join by resistance R 5 and the 2nd pin of U1, the 8th pin meets output z, connect the 3rd pin of multiplier U3, the 9th pin joins by capacitor C 3 and the 8th pin, connects ground connection after 8V DC power supply by resistance R 12, the 13rd pin joins by resistance R 10 and the 14th pin, and the 14th pin joins by resistance R 11 and the 9th pin;
The 1st pin of described multiplier U3 connects the 8th pin of U1, and the 3rd pin connects the 8th pin of U2, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, and the 7th pin connects U1 the 6th pin by resistance R 8, and the 8th pin meets VCC;
The 1st pin of described multiplier U4 connects the 8th pin of U1, and the 3rd pin connects the 7th pin of U1, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, and the 7th pin connects U2 the 13rd pin by resistance R 9, and the 8th pin meets VCC.
Beneficial effect
Useful fruit of the present invention is: at five on the basis of simple three-dimensional chaotic system, a four-dimensional hyperchaotic system without balance point has been proposed, and realize with analog circuit, be applied to the engineering fields such as communication for chaos system a kind of new method and thinking are provided.
Brief description of the drawings
Fig. 1 is the circuit connection structure schematic diagram of the preferred embodiment of the present invention.
Fig. 2 and Fig. 3 are the actual connection layout of circuit of the present invention.
Embodiment
Below in conjunction with accompanying drawing and preferred embodiment, the present invention is further described in detail, referring to Fig. 1-Fig. 3.
1, based on five the four-dimension of simple system without balance point hyperchaotic system, it is characterized in that being, comprise the following steps:
(1) five three-dimensional chaos chaos system i the simplest is:
dx / dt = a ( y - x ) dy / dt = - xz dz / dt = - b + xy i a = 5 , b = 90
(2) on the basis of three-dimensional chaotic system i, increase a differential equation dw/dt=-ky, and w is fed back on second equation of system i, obtain chaos system ii
dz / dt = a ( y - x ) dy / dt = w - xz dz / dt = - b + xy dw / dt = - xy ii a = 10 , b = 80 , k = 10
(3) according to without balance point hyperchaotic system ii constructing analog Circuits System, utilize operational amplifier U1, operational amplifier U2 and resistance and electric capacity to form anti-phase adder and inverting integrator, utilize multiplier U3 and U4 to realize multiplying, utilize 8V DC power supply to realize constant input, described operational amplifier U1 and operational amplifier U2 adopt LF347N, and described multiplier U3 and U4 adopt AD633JN;
Described operational amplifier U1 concatenation operation amplifier U2, multiplier U3, described operational amplifier U2 connects multiplier U4, DC power supply and operational amplifier U1, described multiplier U3 concatenation operation amplifier U1, described multiplier U4 concatenation operation amplifier U2, described 8V DC power supply concatenation operation amplifier U2;
The 1st pin of described operational amplifier U1 joins by resistance R 6 and the 2nd pin, join by resistance R 7 and the 6th pin, the 3rd, 5, 10, 12 pin ground connection, the 4th pin meets VCC, the 11st pin meets VEE, the 6th pin joins by capacitor C 2 and the 7th pin, the 7th pin meets output y, join by resistance R 1 and the 13rd pin, join by resistance R 13 and the 6th pin of U2, connect the 3rd pin of multiplier U4, the 8th pin output x, join by capacitor C 1 and the 9th pin, connect the 1st pin of multiplier U3, connect the 1st pin of multiplier U4, join by resistance R 4 and the 9th pin, the 13rd pin joins by resistance R 2 and the 14th pin, the 14th pin joins by resistance R 3 and the 9th pin,
The 1st, 2 pins of described operational amplifier U2 are unsettled, 3rd, 5,10,12 pin ground connection, the 4th pin meets VCC, the 11st pin meets VEE, the 6th pin joins by capacitor C 4 and the 7th pin, the 7th pin output w, join by resistance R 5 and the 2nd pin of U1, the 8th pin meets output z, connect the 3rd pin of multiplier U3, the 9th pin joins by capacitor C 3 and the 8th pin, connects ground connection after 8V DC power supply by resistance R 12, the 13rd pin joins by resistance R 10 and the 14th pin, and the 14th pin joins by resistance R 11 and the 9th pin;
The 1st pin of described multiplier U3 connects the 8th pin of U1, and the 3rd pin connects the 8th pin of U2, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, and the 7th pin connects U1 the 6th pin by resistance R 8, and the 8th pin meets VCC;
The 1st pin of described multiplier U4 connects the 8th pin of U1, and the 3rd pin connects the 7th pin of U1, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, and the 7th pin connects U2 the 13rd pin by resistance R 9, and the 8th pin meets VCC.
2, based on five the four-dimension of simple system without the analog circuit of balance point hyperchaotic system, it is characterized in that being, formed by operational amplifier U1, operational amplifier U2 and multiplier U3, multiplier U4 and 8V DC power supply;
Described operational amplifier U1 concatenation operation amplifier U2, multiplier U3, described operational amplifier U2 connects multiplier U4, DC power supply and operational amplifier U1, described multiplier U3 concatenation operation amplifier U1, described multiplier U4 concatenation operation amplifier U2, described 8V DC power supply concatenation operation amplifier U2, described operational amplifier U1 and operational amplifier U2 adopt LF347N, and described multiplier U3 and U4 adopt AD633JN;
The 1st pin of described operational amplifier U1 joins by resistance R 6 and the 2nd pin, join by resistance R 7 and the 6th pin, the 3rd, 5, 10, 12 pin ground connection, the 4th pin meets VCC, the 11st pin meets VEE, the 6th pin joins by capacitor C 2 and the 7th pin, the 7th pin meets output y, join by resistance R 1 and the 13rd pin, join by resistance R 13 and the 6th pin of U2, connect the 3rd pin of multiplier U4, the 8th pin output x, join by capacitor C 1 and the 9th pin, connect the 1st pin of multiplier U3, connect the 1st pin of multiplier U4, join by resistance R 4 and the 9th pin, the 13rd pin joins by resistance R 2 and the 14th pin, the 14th pin joins by resistance R 3 and the 9th pin,
The 1st, 2 pins of described operational amplifier U2 are unsettled, 3rd, 5,10,12 pin ground connection, the 4th pin meets VCC, the 11st pin meets VEE, the 6th pin joins by capacitor C 4 and the 7th pin, the 7th pin output w, join by resistance R 5 and the 2nd pin of U1, the 8th pin meets output z, connect the 3rd pin of multiplier U3, the 9th pin joins by capacitor C 3 and the 8th pin, connects ground connection after 8V DC power supply by resistance R 12, the 13rd pin joins by resistance R 10 and the 14th pin, and the 14th pin joins by resistance R 11 and the 9th pin;
The 1st pin of described multiplier U3 connects the 8th pin of U1, and the 3rd pin connects the 8th pin of U2, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, and the 7th pin connects U1 the 6th pin by resistance R 8, and the 8th pin meets VCC;
The 1st pin of described multiplier U4 connects the 8th pin of U1, and the 3rd pin connects the 7th pin of U1, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, and the 7th pin connects U2 the 13rd pin by resistance R 9, and the 8th pin meets VCC.
Resistance R 1=R2=R3=R4=R6=R7=R10=R11=R13=10k Ω in circuit, R8=R9=1k Ω, R5=R12=100k Ω, C1=C2=C3=C4=10nF.
Certainly, above-mentioned explanation is not limitation of the present invention, and the present invention is also not limited only to above-mentioned giving an example, and variation, remodeling, interpolation or replacement that those skilled in the art make in essential scope of the present invention, also belong to protection scope of the present invention.

Claims (2)

  1. Based on five the four-dimension of simple system without balance point hyperchaotic system, it is characterized in that being, comprise the following steps:
    (1) five three-dimensional chaos chaos system i the simplest is:
    dx / dt = a ( y - x ) dy / dt = - xz dz / dt = - b + xy i a = 5 , b = 90
    (2) on the basis of three-dimensional chaotic system i, increase a differential equation dw/dt=-ky, and w is fed back on second equation of system i, obtain chaos system ii
    dz / dt = a ( y - x ) dy / dt = w - xz dz / dt = - b + xy dw / dt = - xy ii a = 10 , b = 80 , k = 10
    (3) according to without balance point hyperchaotic system ii constructing analog Circuits System, utilize operational amplifier U1, operational amplifier U2 and resistance and electric capacity to form anti-phase adder and inverting integrator, utilize multiplier U3 and U4 to realize multiplying, utilize 8V DC power supply to realize constant input, described operational amplifier U1 and operational amplifier U2 adopt LF347N, and described multiplier U3 and U4 adopt AD633JN;
    Described operational amplifier U1 concatenation operation amplifier U2, multiplier U3, described operational amplifier U2 connects multiplier U4, DC power supply and operational amplifier U1, described multiplier U3 concatenation operation amplifier U1, described multiplier U4 concatenation operation amplifier U2, described 8V DC power supply concatenation operation amplifier U2;
    The 1st pin of described operational amplifier U1 joins by resistance R 6 and the 2nd pin, join by resistance R 7 and the 6th pin, the 3rd, 5, 10, 12 pin ground connection, the 4th pin meets VCC, the 11st pin meets VEE, the 6th pin joins by capacitor C 2 and the 7th pin, the 7th pin meets output y, join by resistance R 1 and the 13rd pin, join by resistance R 13 and the 6th pin of U2, connect the 3rd pin of multiplier U4, the 8th pin output x, join by capacitor C 1 and the 9th pin, connect the 1st pin of multiplier U3, connect the 1st pin of multiplier U4, join by resistance R 4 and the 9th pin, the 13rd pin joins by resistance R 2 and the 14th pin, the 14th pin joins by resistance R 3 and the 9th pin,
    The 1st, 2 pins of described operational amplifier U2 are unsettled, 3rd, 5,10,12 pin ground connection, the 4th pin meets VCC, the 11st pin meets VEE, the 6th pin joins by capacitor C 4 and the 7th pin, the 7th pin output w, join by resistance R 5 and the 2nd pin of U1, the 8th pin meets output z, connect the 3rd pin of multiplier U3, the 9th pin joins by capacitor C 3 and the 8th pin, connects ground connection after 8V DC power supply by resistance R 12, the 13rd pin joins by resistance R 10 and the 14th pin, and the 14th pin joins by resistance R 11 and the 9th pin;
    The 1st pin of described multiplier U3 connects the 8th pin of U1, and the 3rd pin connects the 8th pin of U2, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, and the 7th pin connects U1 the 6th pin by resistance R 8, and the 8th pin meets VCC;
    The 1st pin of described multiplier U4 connects the 8th pin of U1, and the 3rd pin connects the 7th pin of U1, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, and the 7th pin connects U2 the 13rd pin by resistance R 9, and the 8th pin meets VCC.
  2. Based on five the four-dimension of simple system without the analog circuit of balance point hyperchaotic system, it is characterized in that being, formed by operational amplifier U1, operational amplifier U2 and multiplier U3, multiplier U4 and 8V DC power supply;
    Described operational amplifier U1 concatenation operation amplifier U2, multiplier U3, described operational amplifier U2 connects multiplier U4, DC power supply and operational amplifier U1, described multiplier U3 concatenation operation amplifier U1, described multiplier U4 concatenation operation amplifier U2, described 8V DC power supply concatenation operation amplifier U2, described operational amplifier U1 and operational amplifier U2 adopt LF347N, and described multiplier U3 and U4 adopt AD633JN;
    The 1st pin of described operational amplifier U1 joins by resistance R 6 and the 2nd pin, join by resistance R 7 and the 6th pin, the 3rd, 5, 10, 12 pin ground connection, the 4th pin meets VCC, the 11st pin meets VEE, the 6th pin joins by capacitor C 2 and the 7th pin, the 7th pin meets output y, join by resistance R 1 and the 13rd pin, join by resistance R 13 and the 6th pin of U2, connect the 3rd pin of multiplier U4, the 8th pin output x, join by capacitor C 1 and the 9th pin, connect the 1st pin of multiplier U3, connect the 1st pin of multiplier U4, join by resistance R 4 and the 9th pin, the 13rd pin joins by resistance R 2 and the 14th pin, the 14th pin joins by resistance R 3 and the 9th pin,
    The 1st, 2 pins of described operational amplifier U2 are unsettled, 3rd, 5,10,12 pin ground connection, the 4th pin meets VCC, the 11st pin meets VEE, the 6th pin joins by capacitor C 4 and the 7th pin, the 7th pin output w, join by resistance R 5 and the 2nd pin of U1, the 8th pin meets output z, connect the 3rd pin of multiplier U3, the 9th pin joins by capacitor C 3 and the 8th pin, connects ground connection after 8V DC power supply by resistance R 12, the 13rd pin joins by resistance R 10 and the 14th pin, and the 14th pin joins by resistance R 11 and the 9th pin;
    The 1st pin of described multiplier U3 connects the 8th pin of U1, and the 3rd pin connects the 8th pin of U2, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, and the 7th pin connects U1 the 6th pin by resistance R 8, and the 8th pin meets VCC;
    The 1st pin of described multiplier U4 connects the 8th pin of U1, and the 3rd pin connects the 7th pin of U1, the equal ground connection of the 2nd, 4,6 pin, and the 5th pin meets VEE, and the 7th pin connects U2 the 13rd pin by resistance R 9, and the 8th pin meets VCC.
CN201410438026.4A 2014-08-31 2014-08-31 Based on the four-dimension of five chaos systems the simplest without the analog circuit of balance point hyperchaotic system Active CN104202143B (en)

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CN201410438026.4A CN104202143B (en) 2014-08-31 2014-08-31 Based on the four-dimension of five chaos systems the simplest without the analog circuit of balance point hyperchaotic system
PCT/CN2015/000261 WO2016029617A1 (en) 2014-08-31 2015-04-14 Four-dimensional non-equilibrium hyperchaotic system and analog circuit, based on five simplest chaotic systems
US15/445,960 US10261975B2 (en) 2014-08-31 2017-02-28 Four-dimensional non-equilibrium hyperchaotic system and analog circuit, based on five simplest chaotic systems

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